# Aptitude - Numbers

### Exercise :: Numbers - General Questions

71.

397 x 397 + 104 x 104 + 2 x 397 x 104 = ?

 A. 250001 B. 251001 C. 260101 D. 261001

Explanation:

 Given Exp. = (397)2 + (104)2 + 2 x 397 x 104 = (397 + 104)2 = (501)2 = (500 + 1)2 = (5002) + (1)2 + (2 x 500 x 1) = 250000 + 1 + 1000 = 251001

72.

(35423 + 7164 + 41720) - (317 x 89) = ?

 A. 28213 B. 84307 C. 50694 D. 56094 E. None of these

Explanation:

```  35423         317 x 89 = 317 x (90 -1 )
+  7164                  = (317 x 90 - 317)
+ 41720                  = (28530 - 317)
-----                  = 28213
84307
- 28213
-----
56094
-----
```

73.

(xn - an) is completely divisible by (x - a), when

 A. n is any natural number B. n is an even natural number C. n is and odd natural number D. n is prime

Explanation:

For every natural number n, (xn - an) is completely divisible by (x - a).

74.

Which one of the following numbers is completely divisible by 45?

 A. 181560 B. 331145 C. 202860 D. 2033555 E. None of these

Explanation:

45 = 5 x 9, where 5 and 9 are co-primes.

Unit digit must be 0 or 5 and sum of digits must be divisible by 9.

Among given numbers, such number is 202860.

75.

Which of the following numbers will completely divide (325 + 326 + 327 + 328) ?

 A. 11 B. 16 C. 25 D. 30

Explanation:

(325 + 326 + 327 + 328) = 325 x (1 + 3 + 32 + 33) = 325 x 40

= 324 x 3 x 4 x 10

= (324 x 4 x 30), which is divisible by30.

76.

A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is:

 A. 0 B. 1 C. 2 D. 3

Explanation:

Let x = 6q + 3.

Then, x2 = (6q + 3)2

= 36q2 + 36q + 9

= 6(6q2 + 6q + 1) + 3

Thus, when x2 is divided by 6, then remainder = 3.

77.

The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?

A.
 12 35
B.
 1 35
C.
 35 8
D.
 7 32

Explanation:

Let the numbers be a and b. Then, a + b = 12 and ab = 35. a + b = 12  1 + 1 = 12 ab 35 b a 35 Sum of reciprocals of given numbers = 12 35

78.

What will be remainder when 17200 is divided by 18 ?

 A. 17 B. 16 C. 1 D. 2

Explanation:

When n is even. (xn - an) is completely divisibly by (x + a)

(17200 - 1200) is completely divisible by (17 + 1), i.e., 18. (17200 - 1) is completely divisible by 18. On dividing 17200 by 18, we get 1 as remainder.

79.

If 1400 x x = 1050. Then, x = ?

A.
 1 4
B.
 3 5
C.
 2 3
D.
 3 4
E. None of these

Explanation:

 1400 x x = 1050 x = 1050 = 3 1400 4

80.

(12 + 22 + 32 + ... + 102) = ?

 A. 330 B. 345 C. 365 D. 385

Explanation:

 We know that (12 + 22 + 32 + ... + n2) = 1 n(n + 1)(2n + 1) 6

 Putting n = 10, required sum = 1 x 10 x 11 x 21 = 385 6